text: The process of population relaxation refers to nuclear spins that return to thermodynamic equilibrium in the magnet. This process is also called T, "spin-lattice" or "longitudinal magnetic" relaxation, where T refers to the mean time for an individual nucleus to return to its thermal equilibrium state of the spins. After the nuclear spin population has relaxed, it can be probed again, since it is in the initial, equilibrium (mixed) state.
  The precessing nuclei can also fall out of alignment with each other and gradually stop producing a signal. This is called T or transverse relaxation. Because of the difference in the actual relaxation mechanisms involved (for example, intermolecular versus intramolecular magnetic dipole-dipole interactions ), T is usually (except in rare cases) longer than T (that is, slower spin-lattice relaxation, for example because of smaller dipole-dipole interaction effects). In practice, the value of T* which is the actually observed decay time of the observed NMR signal, or free induction decay (to  of the initial amplitude immediately after the resonant RF pulse), also depends on the static magnetic field inhomogeneity, which is quite significant. (There is also a smaller but significant contribution to the observed FID shortening from the RF inhomogeneity of the resonant pulse). In the corresponding FT-NMR spectrum—meaning the Fourier transform of the free induction decay—the T* time is inversely related to the width of the NMR signal in frequency units. Thus, a nucleus with a long T relaxation time gives rise to a very sharp NMR peak in the FT-NMR spectrum for a very homogeneous ("well-shimmed") static magnetic field, whereas nuclei with shorter T values give rise to broad FT-NMR peaks even when the magnet is shimmed well. Both T and T depend on the rate of molecular motions as well as the gyromagnetic ratios of both the resonating and their strongly interacting, next-neighbor nuclei that are not at resonance.
  A Hahn echo decay experiment can be used to measure the dephasing time, as shown in the animation. The size of the echo is recorded for different spacings of the two pulses. This reveals the decoherence that is not refocused by the 180° pulse. In simple cases, an exponential decay is measured which is described by the T time.